Question

The graph of Flx) can be compressed vertically and shifted to the right toproduce the graph of G(X). If F(X) = x, which of the following could be theequation of G(x)?O A. GX) = *+B. G(X) = 2(x=69O C. G(X) = 36-6)D. G(X) = 212-6)

Answer 1

Hello there. To solve this question, we need to remember some properties on functions and their graphs.

Starting with the function f(x) = x², we want to find a function g(x) such that it represents a shifted to the right and compressed vertically version of f(x).

First, graph f(x) and see what you want to have:

Shift a quadratic function to the right means changing the place of its vertex. In fact, for f(x), we can subtract values inside the square, or complete the square and then do it.

Notice that (x - a)² is a quadratic function with root a. If a is greater than 0, we have the case of the graph below:

So, when we want to shift to the right, you subtract a positive number. If you want to shift it to the left, subtract a negative number, thus it becomes a plus.

Now, talking about compressing it. We'd have something like follows:

This happens when we multiply the function by a factor between 0 and 1.

If the factor is less than 0, it will turn the parabola upside down (works for all types of graphs) and if it is greater than 1, it'll stretch the parabola, becoming bigger and not compressed.

In the options we have, the only option that satisfies both compressed vertically and shifted to the right version of f(x) is G(x) = 1/2 * (x - 6)².